Numerical studies are conducted to describe the time-dependent adjustment of natural convection in a square cavity. The two vertical sidewalls are maintained at different temperatures, which is represented by the external Rayleigh number $Ra_E$. A uniform internal heat generation, which is denoted by the internal Rayleigh number $Ra_I$, is switched-on impulsively at t=0. The resulting time-dependent process of settlement to the final-state for large $Ra_E$ and $Ra_I$, Pr~O(1) is depicted by solving numerically the governing equations. When the value of $Ra_I$ and $Ra_E$ are comparable, the major circulation cell is little affected by the internal heating. When $Ra_I$/$Ra_E$ is moderately large, an additional oppositely-directed circulation cell appears in the upper corner of the heat sidewall. When $Ra_I$/$Ra_E$ is large, three separate stages are seen. In the last stage, the whole cavity is occupied by two oppositely-directed circulation cells. The final-state features are consistent with the preceding experimental observations. By inspecting the time histories of the average Nusselt number on the wall, the overall time characterizing the global adjustment is shown to scale with $Ra_I^{-1/4}$. Analysing the time histories at selected points in the cavity, when $Ra_I$/$Ra_E$ is large, oscillatory motion is shown in the approach to steady-state. But when the value of $Ra_I$ and $Ra_E$ are comparable and $Ra_I$/$Ra_E$ is appreciable, oscillatiry behavior is not evident.
